A Mathematical Model for Intracellular HIV-1 Gag Protein Transport and its Parallel Numerical Simulations

In this paper, we develop a mathematical model for intracellular HIV-1 gag protein tracking based on the hypotheses that gag proteins employ kinesins for active transport on microtubules and they can also diffuse in cytoplasm. This results in a time-dependent convection-diffusion equation in polar coordinates along with appropriate boundary and initial conditions. A finite element method based on tracking characteristics is established for accurately solving this type of transport problems. The numerical method has been implemented in C++. To validate the mathematical model, we perform numerical simulations on the virion timing, i.e., the time needed for HIV-1 virions (puncta) to first appear on the cell plasma membrane. Numerical simulation results and biological experimental data agree principally. For in silico analysis of gag protein tracking, the numerical simulation code needs to be executed repeatedly on a large collection of sets of model parameters. We further investigate code parallelization strategies using MPI and OpenMP.